Rigidity checking method and apparatus with the result freed from the influence of picture resolutions

ABSTRACT

A rigidity checking method and apparatus is presented. A composite feature vector is first generated by combining three pairs of coordinates obtained for a feature point of a target object from three pictures of the target object. A covariance matrix of the compound feature vector is calculated by finding a product of a variance matrix comprising a variance of each element of the compound feature vector and the transposed matrix of the variance matrix. The rigidity of the target object is calculated by using the element of the covariance matrix and compared with a predetermined threshold to determine whether the target object is a rigid body. Thus, a rigidity checking is directly achieved from the joint distribution of feature points in the three pictures without assuming the coefficients of a set of constraint equations.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a rigidity checking method andapparatus for effectively checking the rigidity of an object perceivedby a automated robot of vehicle, or of an object indruding into thesensing field of monitor camera.

2. Description of the Prior Art

The distance between two arbitrary points on a rigid body remainsunchanged even when the rigid body takes a force or moves. This propertyof the rigid body permits a decision to be made from an image sequenceincluding a target body as to whether the target body is a rigid body ornot.

A rigidity checking technique is described in detail by S. Ullman and R.Basri, Object Recognition by Liner Combination of the Model, IEEE Trans.PAMI (Pattern Analysis and Machine Intelligence). In this technique,assuming three pairs of coordinates of a feature point of the targetobject in three pictures taken at different times to be (X₁, Y₁), (X₂,Y₂) and (X₃, Y₃), tests are made to see to what extent the coordinates(X₁, Y₁), (X₂, Y₂) and (X₃, Y₃) satisfy the following linear constraintequations:

    α.sub.1.sup.1 S.sub.1 +β.sub.1.sup.1 Y.sub.1 +γ.sub.1.sup.1 X.sub.2 +ω.sub.1.sup.1 X.sub.3 =0, (1)

    α.sub.1.sup.2 X.sub.1 +β.sub.1.sup.2 Y.sub.1 +γ.sub.1.sup.2 Y.sub.2 +ω.sub.1.sup.2 Y.sub.3 =0, (2)

    α.sub.2.sup.1 X.sub.1 +β.sub.2.sup.1 X.sub.2 +γ.sub.2.sup.1 Y.sub.2 +ω.sub.2.sup.1 X.sub.3 =0, (3)

    α.sub.2.sup.2 X.sub.1 +β.sub.2.sup.2 X.sub.2 +γ.sub.2.sup.2 Y.sub.2 +ω.sub.2.sup.2 X.sub.3 =0, (4)

    α.sub.3.sup.1 X.sub.1 +β.sub.3.sup.1 X.sub.2 +γ.sub.3.sup.1 Y.sub.3 +ω.sub.3.sup.1 X.sub.3 =0, and (5)

    α.sub.3.sup.2 X.sub.1 +β.sub.3.sup.2 X.sub.2 +γ.sub.3.sup.2 Y.sub.3 +ω.sub.3.sup.2 X.sub.3 =0, (6)

where α_(i) ^(j), β_(i) ^(j), γ_(i) ^(j) and κ_(i) ^(j) are appropriatecoefficients. Since a rigid body satisfies these constraint equations,the rigidity of the target object can be estimated by the extent towhich the three pairs of coordinates satisfies the above constraintequations, that is, a satisfaction degree of the constraint equation.

In order to estimate the satisfaction degree, the optimum values areconventionally found for the coefficients of the constraint equations bymeans of least square error estimate by using a sufficient number offeature points. Then, the residue of each constraint equation iscalculated as a satisfaction degree. It is determined that the smallerthe residues or the satisfaction degrees are, the more rigidity thetarget object has.

However, the values of the constraint equations changes with a change inthe resolutions of the three pictures. Since the resolutions of thepictures which have essentially nothing to do with the rigidity of thetarget object have effects on a judgement of the rigidity of the targetobject, the conventional rigid checking technique is not suitable for ageneral purpose tool.

Further, the conventional rigid checking technique requires calculationsof the coefficients of the constraint equations which have no directrelationships with the rigidity of the target object, and accordingly isnot effective.

SUMMARY OF THE INVENTION

It is therefore an object of the invention to provide a rigiditychecking method and apparatus which has a raised efficiency and permitsa wide use.

According to the present invention, a composite feature vector is firstgenerated by combining three pairs of coordinates obtained for a featurepoint of a target object from three pictures of the target object; acovariance matrix of the compound feature vector is calculated byfinding a product of a variance matrix comprising a variance of eachelement of the compound feature vector and the transposed matrix of thevariance matrix; the rigidity of the target object is calculated byusing the element of the covariance matrix; and the rigidity is comparedwith a predetermined threshold to determine whether the target object isa rigid body. Thus, a rigidity checking is directly achieved from thejoint distribution of feature points in the three pictures withoutrecovering the coefficients of a set of constraint equations forestimating the residue of each constraint equation as done in the priorart.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects and advantages of the present invention will be apparentfrom the following description of the preferred embodiments of theinvention as illustrated in the accompanying drawings. In the drawings:

FIG. 1 is a block diagram showing a first illustrative embodiment of anobject chasing system incorporating a rigidity checking apparatusrealized with dedicated hardware according to the present invention;

FIG. 2 is a block diagram showing a second illustrative embodiment of anobject chasing system incorporating a rigidity checking apparatusrealized with a microcomputer according to the present invention; and

FIG. 3 is a flow chart showing a flow of a rigidity checking operationexecuted by each of the apparatuses shown in FIG. 1 and 2.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a block diagram showing a first illustrative embodiment of anobject chasing system incorporating a rigidity checking apparatusrealized with dedicated hardware according to the present invention. InFIG. 1, the object chasing system 1 comprises a self-propelled objectchasing unit 170, a camera 100 mounted on the object chasing unit 170,an image memory 120 for storing images supplied from the camera 100, afeature point extractor 130 for extracting a feature point of a targetobject from three images in the image memory 120 and complete a compoundfeature vector, a covariance matrix generator 140 for calculating acovariance matrix from the compound feature vector, a rigiditycalculator 150 for calculating the rigidity of the target object bysuing a equation comprising a combination of elements of the covariancematrix, and a controller 160 for controlling the object chasing unit 170in response to the result of the rigidity checking by a comparison ofthe calculated rigidity with a predetermined threshold. The comparisonmay be executed by either the rigidity calculator 150 of the controller160. The controller 160 comprises a central processing unit (CPU) 162, aread only memory (ROM) 164 for storing a program and data, a randomaccess memory (RAM) 166, and an input and output interface (I/O IF) 168as well known in the art.

A similar object chasing system may be realized by using a microcomputeras shown in FIG. 2 instead of dedicated hardware such as the featurepoint extractor 130, the covariance generator 140 and the rigiditycalculator 150. FIG. 2 is a block diagram showing a second illustrativeembodiment of an object chasing system incorporating a rigidity checkingapparatus realized with a microcomputer according to the presentinvention. In FIG. 2, the object chasing system 2 comprising a camera100, an image memory 120, an input interface (IF) 222 through which animage data is supplied from the camera 100 to the memory 120, amicrocomputer 260 for performing a rigidity checking, and an objectchasing unit 270 which includes a controller (not shown) for controllingthe unit 270 itself. The microcomputer 260 comprises a CPU 262, a ROM262 for storing a program and data for rigidity checking, a RAM 266, anoutput interface 224 through which the image data is read from thememory 120, and an input and output interface (I/O IF) 268 through whichthe CPU 262 communicates with the controller (not shown) of the unit270.

FIG. 3 is a flow chart showing a flow of a rigidity checking operationexecuted by the elements 130, 140, 150 and 162 in case of the apparatus1 of FIG. 1 and by CPU 266 under the control of the program stored inROM 266 in case of the apparatus 2 of FIG. 2. Therefore, the rigiditychecking operation will be described referring to FIG. 1 and 3 in thefollowing, where a description corresponding to any of the steps of FIG.3 is indicated by a step number in parentheses.

An two-dimension (2-D) image of a target object is supplied to thememory 120 from the camera 100 mounted on the object chasing unit 170(or 270).

Among the frames supplied from the camera 100, the feature pointextractor 130 selects three frames in which the target object has movedsufficiently in distance, N+1 features points on the target object areselected from a first one of the three selected frames, correspondingN+1 feature points are found from each of the two remaining frames, andN 2-D feature point vectors from one of the N+1 feature points to the Nother feature points are found for each of the three frames (step 300)and expressed as:

     Xn.sub.1, Yn.sub.1 !

     Xn.sub.2, Yn.sub.2 ! and

     Xn.sub.3, Yn.sub.3 !

where n=1 . . . , N. Then, the feature point extractor 130 generates N6-D compound feature vectors Xn₁, Xn₂, Yn₂, Xn₃, Yn₃ ! (step 310) bycombining, for each of N feature points, three feature point vectors forthe three frames into one vector.

The covariance matrix generator 140 generates the following covariancematrix (step 320):

    C≡ΣUn.sup.T *Un (Σ means a summation for n=1, . . . , N) (7)

where Un≡(Xn₁ -<X₁ >, Yn₁ -<Y₁ >, Xn₂ -X₂ >, Yn₂ -<Y₂ >, Xn₃ -<X₃ >, Yn₃-<Y₃ >), M^(T) is a transposed matrix of M, and <X_(i) > and <Y_(i) >are means of Xn_(i) and Yn_(i), respectively, that is:

    <X.sub.i >=(1/N)ΣXn.sub.i

    <Y.sub.i >=(1/N)ΣYn.sub.i

where Σ is a summation for n=1, . . . , N.

By using the covariance matrix and variances of coordinates of thefeature points, the rigidity calculator 150 calculates a rigidity R ofthe target object (step 330):

    R=1-(R.sub.1.sup.1 +R.sub.1.sup.2 +R.sub.2.sup.1 R.sub.2.sup.2 +R.sub.3.sup.1 +R.sub.3.sup.2)/6,                         (8)

where

R₁ ¹ ≡det(C1)/(det(C2)C₃₃ C₅₅),

R₁ ² ≡det(C3)/(det(C2)C₄₄ C₆₆),

R₂ ¹ ≡det(C4)/(det(C5)C₁₁ C₅₅),

R₂ ² ≡det(C6)/(det(C5)C₂₂ C₆₆),

R₃ ¹ ≡det(C7)/(det(C8)C₁₁ C₃₃), and

R₃ ² ≡det(C9)/(det(C8)C₂₂ C₄₄),

where det (M) is a determinant of matrix M, C_(ij) is an (i,j) elementof the covariance matrix C, and C1 through C9 are square matricesexpressed as follows: ##EQU1##

The rigidity calculator 150 compares the calculated rigidity R with apredetermined threshold to see if the rigidity R is equal to or largerthan the threshold. If so, the calculator 150 sends a signal indicativeof a rigid body to the CPU 162, and otherwise sends the opposite signalindicative of a unrigid body to the CPU 162.

Alternatively, the rigidity calculator 150 sends the calculated rigidityR as it is to the CPU 162, which in turn compares the calculatedrigidity R with a predetermined threshold to see if the rigidity R isequal to or larger than the threshold (step 340). If so, the CPU 162determines that the target object is a rigid body (step 350), andotherwise determines that the target body is an unrigid body (step 360).

Subsequently, the CPUs 162 and 262 operate according to the result ofthe rigidity check.

Since the equation (8) has been used for estimating the rigidity, thepropriety of the equation (8) will be described in the following.

As described above, if the target object is a rigid body, the componentsof the feature point vectors Xn₁, Yn₁ !, Xn₂, Yn₂ ! and Xn₃, Yn₃ ! willsatisfy the above mentioned equations (1) through (6). Among theequations (1) through (6), Equations (1) and (2) concern the featurepoint Xn₁, Yn₁ !, equations (3) and (4) concern the feature point Xn₂,Yn₂ !, and equations (3) and (4) concern the feature point Xn₃, Yn₃ !.

It is well known as a property of Gramian (Gram determinant) that theequation (1) is equivalent to det C1!. (See, for example, "Matrix Theoryfor System Control." Measurement and Automatic Control Society (ofJapan) pp. 136-137.) That is,

    α.sub.1.sup.1 X.sub.1 +β.sub.1.sup.1 Y.sub.1 +γ.sub.1.sup.1 X.sub.2 +ω.sub.1.sup.1 X.sub.3 =0<--> det C1!=0 (10)

For the sake of simplicity, only one feature point is considered here.For this reason,

It is also well known from the geometric point of view that det C1! is aquantity indicating the volume defined by four dimensional extent of thevector field of the vector X₁, Y₁, X₂, X₃ ! and that det C1! is suitablefor a quantity for estimating the dimensional degeneracy (degeneracyfrom four-dimensional extent to three-dimensional extent).

The meaning of the constraint equation remains unchanged even if theequation (1) is converted into the following equation by normalizing thedistribution of the features contained in the equation (1):

    a.sub.1.sup.1 X.sub.1 '+b.sub.1.sup.1 Y.sub.1 '+e.sub.1.sup.1 X.sub.2 '+f.sub.1.sup.1 X.sub.3 '=0,                              (11)

where there are following relations between X₁ ', Y₁ ' and X₁, Y₁, andbetween a₁ ¹, b₁ ¹ and α₁ ¹ +β₁ ¹ : ##EQU2## where A=Λ^(-1/2)ΦT,

where Λ, Φ are respectively a proper matrix and a characteristic vectormatrix of a matrix: ##EQU3## and Λ^(-1/2) is an inverse matrix of asquare root matrix of the matrix Λ.

    (a.sub.1.sup.1 b.sub.1.sup.1)≡(α.sub.1.sup.1 β.sub.1.sup.1)A.sup.-1

Further,

X₂ '=C₃₃ ^(-1/2) X₂,

e₁ ¹ =γ₁ ¹ C₃₃ ^(1/2),

X₃ '=C₅₅ ^(-1/2) X₃, and

f₁ ¹ =Ω₁ ¹ C₅₅ ^(1/2).

Carrying out the above normalization not only prevents the estimationequation from being affected by the resolution of the frame in whichfeature points are recorded but also prevents the distribution of thefeature points ((X₁, Y₁) in case of equation (11)) in the image planefrom being subjected to a dimensional degeneracy.

Since estimating the determinant det C1!=0 of the 4×4 covariance matrixof the vector composed of newly normalized distribution X₁, Y₁ !, X₂ !and X₃ ! is equivalent to estimating the equation (1), in order for thevalue of det C1! to be normalized into 0 through 1 in an estimation ofthe degree of satisfying det C1!=0, the rigidity of the target isdefined on the basis of the constraint equation (1) by the followingexpression:

    1-(σ.sub.1 σ.sub.2 σ.sub.3 σ.sub.4 /((σ.sub.1 +σ.sub.2 +σ.sub.3 +σ.sub.4)/4).sup.4),  (12)

where σ₁, σ₂, σ₃ and σ₄ are eigenvalues of the covariance matrix for (X₁', Y₁ ', X₂ ', X₃ ') in equation (11).

It is vary well known as Schwarz's inequality that the equation (12) hasbeen normalized into 0 through 1.

Finally, arranging the equation (12) yields:

    1-det C1!/det C2!C.sub.33 C.sub.55.                        (13)

where C1, C2, C₃₃ and C₅₅ are the same as those defined in conjunctionwith equations (9) and (7).

Since the same discussion can be applied to equations (2) through (6),the estimated value of the rigidity can be obtained by taking a mean ofthe estimates based on the constraint equations.

It is equation (2) that takes the mean. Therefore, in calculating therigidity, the degree of the feature points satisfying the constraintequation which characterizes the property of a rigid body is calculatedby combining the components of the covariance matrix. In other words, arigidity checking system according to the invention judges the rigidityof a target directly from the joint distribution of the feature pointsinstead of assuming the coefficients of the constraint equation andestimating the rigidity by using the residues of the constraint equationas in the prior art.

Also, normalizing, arranging and taking a means for each combination ofconstraint equations (1) and (2) concerning the feature point (X₁, Y₁),constraint equations (3) and (4) concerning corresponding feature point(X₂, Y₂), and constraint equations (5) and (6) concerning the featurepoint (X₃, Y₃) yields the following expression as an expression forcalculating the rigidity of the target object:

    1-(R.sub.1 +R.sub.2 +R.sub.3)/3,                           (14)

where

R₁ ≡{det{C1}+det{C3}}/{det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)},

R₂ ≡{det{C4}+det {C6}}/det{det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)}, and

R₃ ≡{det{C7}+det{C9}}/{det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)}.

The rigidity of the target object may be calculated by using theequation (14).

Normalizing, arranging and taking a means for the entirety of theconstraint equations (1) through (6) yields the following expression asan expression for calculating the rigidity of the target object:

    1-R.sub.0,                                                 (15)

where

R₀ ={det{C1}+det {C3}+det{C4}+det {C6}+det{C7}+det{C9}}/{det{C2}(C₃₃ C₅₅+C₄₄ C₆₆)+det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)+det {C8}(C₁₁ C₃₃ +C₂₂ C₄₄)}.

The rigidity of the target object may be calculated by using theequation (15).

Instead of using equation (8), the rigidity of the target object may becalculated by using the following equation:

    Q.sub.1.sup.1 +Q.sub.1.sup.2 +Q.sub.2.sup.1 +Q.sub.2.sup.2 +Q.sub.3.sup.1 +Q.sub.3.sup.2,                                           (16)

where

Q₁ ¹ ≡{(1-k)det{C2}C₃₃ C₅₅ -det{C1}}/(1-k)det{C2}C₃₃ C₅₅,

Q₁ ² ≡{(1-k)det{C2}C₄₄ C₆₆ -det{C3}}/(1-k)det{C2}C₄₄ C₆₆,

Q₂ ¹ ≡{(1-k)det{C5}C₁₁ C₅₅ -det{C4}}/(1-k)det{C5}C₁₁ C₅₅,

Q₂ ² ≡{(1-k)det{C5}C₂₂ C₆₆ -det{C6}}/(1-k)det{C5}C₂₂ C₆₆,

Q₃ ¹ ≡{(1-k)det{C8}C₁₁ C₃₃ -det{C7}}/(1-k)det{C8}C₁₁ C₃₃,

and

Q₃ ² ≡{(1-k)det{C8}C₂₂ C₄₄ -det{C9}}/(1-k)det{C8}C₂₂ C₄₄,

where k is a constant and 0<k<1. In this case, the rigidity of thetarget can be properly calculated by adjusting the value of k.

The rigidity of the target object may be calculated by suing thefollowing equation into which the equation (14) has been modified:

    Q.sub.1 +Q.sub.2 +Q.sub.3,                                 (17)

where

Q₁ ={(1-k)det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)-(det{C1}+det{C3})}/(1-k)det{C2}(C₃₃C₅₅ +C₄₄ C₆₆),

Q₂ ={(1-k)det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)-(det{C4}+det{C6})}/(1-k)det{C5}(C₁₁C₅₅ +C₂₂ C₆₆), and

Q₃ ={(1-k)det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)-(det{C7}+det{C9})}/(1-k)det{C8}(C₁₁C₃₃ +C₂₂ C₄₄).

The rigidity of the target object may be calculated by using thefollowing equation into which the equation (15) has been modified:##EQU4## If equation (17) or (18) is used, the rigidity of the targetobject can be properly calculated by adjusting the value of k.

Many widely different embodiments of the present invention may beconstructed without departing from the spirit and scope of the presentinvention. It should be understood that the present invention is notlimited to the specific embodiments described in the specification,except as defined in the appended claims.

What is claimed is:
 1. In a rigidity checking system wherein a rigidity checking is achieved by using three pictures in which a target object is recorded as substantially moved in distance, a method of checking the rigidity R of the target object without being affected by the resolution of the pictures, comprising the steps of:selecting N feature points of said target object and, for each of said N feature points, generating a 6-D compound feature vector from three 2-D feature vectors each indicative of the position of said feature point in corresponding one of said three pictures; calculating a sum of a covariance matrix of each of said compound feature vectors for said N feature points to provide a summed covariance matrix C; calculating said rigidity R by using components of said summed covariance matrix C; and comparing said rigidity R with a predetermined threshold to determine whether said target object is a rigid body or not.
 2. A method as defined in claim 1, wherein said three feature vectors are Xn₁, Yn₁ !, Xn₂, Yn₂ ! and Xn₃, Yn₃ !, where n=1, . . . , N and 1, 2 and 3 corresponds to said three pictures and wherein:said generating a 6-D compound feature vector comprises generating a vector Xn₁, Yn₁, Xn₂, Yn₂, Xn₃ !; and said step of calculating a sum comprises the steps of: calculating said summed covariance matrix C as follows:

    C≡ΣUn.sup.T *Un.

where Σ indicates a summation for n=1, . . . , N, Un=(Xn₁ -<X₁ >, Yn₁ -<Y₁ >, Xn₂ -<X₂ >, Yn₂ -<Y₂ >, Xn₃ -<X₃ >, Yn₃ -<Y₃ >), and M^(T) is a transposed matrix of M, where

    <X.sub.i >=(1/N)ΣXn.sub.i

    <Y.sub.1 >=(1/N)ΣYn.sub.i

(Σ is a summation for n=1, . . . , N.); and calculating, for subsequent use, the following square matrices: ##EQU5##
 3. A method as defined in claim 2, wherein said step of calculating the rigidity R comprises the step of calculating:

    R=1-(R.sub.1.sup.1 +R.sub.1.sup.2 +R.sub.2.sup.1 +R.sub.2.sup.2 +R.sub.3.sup.1 +R.sub.3.sup.2)/6,

where R₁ ¹ ≡det{C1}/ (det{C2}C₃₃ C₅₅), R₁ ² ≡det{C3}/ (det{C2}C₄₄ C₆₆), R₂ ¹ ≡det{C4}/ (det{C5}C₁₁ C₅₅), R₂ ² ≡det{C6}/ (det{C5}C₂₂ C₆₆), R₃ ¹ ≡det{C7}/ (det{C8}C₁₁ C₃₃), and R₃ ² ≡det{C9}/ (det{C8}C₂₂ C₄₄),where det{M} is a determinant of matrix M, C_(ij) is an ij-element of said summed covariance matrix C.
 4. A method as defined in claim 2, wherein said step of calculating the rigidity R comprises the step of calculating:

    R=1-(R.sub.1 +R.sub.2 +R.sub.3)/3,

where R₁ ≡{det{C1}+det{C3}}/(det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)}, R₂ ≡{det{C4}+det{C6}}/(det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)}, and R₃ ≡{det{C7}+det{C9}}/(det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)}.
 5. A method as defined in claim 2, whereinsaid step of calculating the rigidity R comprises the step of calculating:

    R=1˜R.sub.0,

where R₀ ={det{C1}+det{C3}+det{C4}+det {C6}+det{C7}+det{C9}}/{det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)+det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)+det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)}.
 6. A method as defined in claim 2, wherein said step of calculating the rigidity R comprises the step of calculating:

    R=Q.sub.1.sup.1 +Q.sub.1.sup.2 +Q.sub.2.sup.1 +Q.sub.2.sup.2 +Q.sub.3.sup.1 +Q.sub.3.sup.2,

where Q₁ ¹ ≡{(1-k)det{C2}C₃₃ C₅₅ -det{C1}}/(1-k)det{C2}C₃₃ C₅₅, Q₁ ² ≡{(1-k)det{C2}C₄₄ C₆₆ -det{C3}}/(1-k)det{C2}C₄₄ C₆₆, Q₂ ¹ ≡{(1-k)det{C5}C₁₁ C₅₅ -det{C4}}/(1-k)det{C5}C₁₁ C₅₅, Q₂ ² ≡{(1-k)det{C5}C₂₂ C₆₆ -det{C6}}/(1-k)det{C5}C₂₂ C₆₆, Q₃ ¹ ≡{(1-k)det{C8}C₁₁ C₃₃ -det{C7}}/(1-k)det{C8}C₁₁ C₃₃, and Q₃ ² ≡{(1-k)det{C8}C₂₂ C₄₄ -det{C9}}/(1-k)det{C8}C₂₂ C₄₄,where k is a constant that satisfies 0<k<1.
 7. A method as defined in claim 2, wherein said step of calculating the rigidity R comprises the step of calculating:

    R=Q.sub.1 +Q.sub.2 +Q.sub.3,

where Q₁ ≡{(1-k)det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)-(det{C1}+det{C3})}/(1-k)det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆), Q₂ ≡{(1-k)det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)-(det{C4}+det{C6})}/(1-k)det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆), and Q₃ ≡{(1-k)det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)-(det{C7}+det{C9})}/(1-k)det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄).
 8. A method as defined in claim 2, wherein said step of calculating the rigidity comprises the step of calculating: ##EQU6##
 9. An apparatus, which uses three pictures in which a target object is recorded as substantially moved in distance, for checking the rigidity R of the target object without being affected by the resolution of the pictures, the apparatus comprising:means for selecting N feature points of said target object and for generating, for each of said N feature points, a 6-D compound feature vector from three 2-D feature vectors each indicative of the position of said feature point in corresponding one of said three pictures; means for calculating a sum of a covariance matrix of each of said compound feature vectors for said N feature points to provide a summed covariance matrix C; means for calculating said rigidity R by using components of said summed covariance matrix C; and means for comparing said rigidity R with a predetermined threshold to determine whether said target object is a rigid body or not.
 10. An apparatus as defined in claim 9, wherein said three feature vectors are Xn₁, Yn₁ !, Xn₂, Yn₂ ! and Xn₃, Yn₃ !, where n=1, . . . , N and 1, 2 and 3 corresponds to said three pictures and wherein:said means for generating a 6-D compound feature vector comprises means for generating a vector Xn₁, Yn₁, Xn₂, Yn₂, Xn₃, Yn₃ !; and said means for calculating a sum comprises: means for calculating said summed covariance matrix C as follows:

    C≡ΣUn.sup.T *Un,

where Σ indicates a summation for n=1, . . . , N, Un≡(Xn₁ -<X₁ >, Yn₁ -<Y₁ >, Xn₂ -<X₂ >, Yn₂ -<Y₂ >, Xn₃ -<X₃ >, Yn₃ -<Y₃ >), and M^(T) is a transposed matrix of M, where

    <X.sub.i >=(1/N)ΣXn.sub.i

    <Y.sub.i >=(1/N)ΣYn.sub.i

(Σ is a summation for n=1, . . . , N.); and means for calculating, for subsequent use, the following square matrices: ##EQU7##
 11. An apparatus as defined in claim 10, wherein said means for calculating the rigidity R comprises means for calculating:

    R=1-(R.sub.1.sup.1 +R.sub.1.sup.2 +R.sub.2.sup.1 +R.sub.2.sup.2 +R.sub.3.sup.2)/6,

where R₁ ¹ ≡det{C1}/(det{C2}C₃₃ C₅₅), R₁ ² ≡det{C3}/(det{C2}C₄₄ C₆₆), R₂ ¹ ≡det{C4}/(det{C5}C₁₁ C₅₅), R₂ ² ≡det{C6}/(det{C5}C₂₂ C₆₆), R₃ ¹ ≡det{C7}/(det{C8}C₁₁ C₃₃), and R₃ ² ≡det{C9}/(det{C8}C₂₂ C₄₄),where det{M} is a determinant of matrix M, C_(ij) is an ij-element of said summed covariance matrix C.
 12. An apparatus as defined in claim 10, wherein said means for calculating the rigidity R comprises means for calculating:

    R=1-(R.sub.1 +R.sub.2 +R.sub.3)/3,

where R₁ ≡{det{C1}+det{C3}}/{det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)}, R₂ ≡{det{C4}+det{C6}}/{det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)}, and R₃ ≡{det{C7}+det{C9}}/{det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)}.
 13. An apparatus as defined in claim 10, wherein said means for calculating the rigidity R comprises means for calculating:

    R=1-R.sub.0,

where R₀ ={det{C1}+det{C3}+det{C4}+det{C6}+det{C7}+det{C9}}/{det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)+C₄₄ C₆₆)+det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)+det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)}.
 14. An apparatus as defined in claim 10, wherein said means for calculating the rigidity R comprises means for calculating:

    R=Q.sub.1.sup.1 +Q.sub.1.sup.2 +Q.sub.2.sup.1 +Q.sub.2.sup.2 +Q.sub.3.sup.1 +Q.sub.3.sup.2,

where Q₁ ¹ ≡{(1-k)det{C2}C₃₃ C₅₅ -det{C1}}/(1-k)det {C2}C₃₃ C₅₅, Q₁ ² ≡{(1-k)det{C2}C₄₄ C₆₆ -det{C3}}/(1-k)det {C2}C₄₄ C₆₆, Q₂ ¹ ≡{(1-k)det{C5}C₁₁ C₅₅ -det{C4}}/(1-k)det {C5}C₁₁ C₅₅, Q₂ ² ≡{(1-k)det{C5}C₂₂ C₆₆ -det{C6}}/(1-k)det {C5}C₂₂ C₆₆, Q₃ ¹ ≡{(1-k)det{C8}C₁₁ C₃₃ -det{C7}}/(1-k)det {C8}C₁₁ C₃₃, and Q₃ ² ≡{(1-k)det{C8}C₁₁ C₃₃ -det{C9}}/(1-k)det {C8}C₂₂ C₄₄,where k is a constant that satisfied 0<k<1.
 15. An apparatus as defined in claim 10, wherein said means for calculating the rigidity R comprises means for calculating:

    R=Q.sub.1 +Q.sub.2 +Q.sub.3,

where Q₁ ={(1-k)det{C2}(C₃₃ C₅₅ +C₄₄ C₆₆)-(det{C1}+det{C3})}/(1-k)det {C2}(C₃₃ C₅₅ +C₄₄ C₆₆), Q₂ ={(1-k)det{C5}(C₁₁ C₅₅ +C₂₂ C₆₆)-(det{C4}+det{C6})}/(1-k)det {C5}(C₁₁ C₅₅ +C₂₂ C₆₆), and Q₃ ={(1-k)det{C8}(C₁₁ C₃₃ +C₂₂ C₄₄)-(det{C7}+det{C9})}/(1-k)det {C8}(C₁₁ C₃₃ +C₂₂ C₄₄).
 16. An apparatus as defined in claim 10, wherein said means for calculating the rigidity comprises means for calculating: ##EQU8##
 17. A self-propelled robot provided with an apparatus as defined in claim 9, the robot comprising:means for supplying said selecting and generating means with images of said target object; a controller for controlling the robot in response to the determination by said comparing means.
 18. A self-propelled vehicle provided with an apparatus as defined in claim 9, the vehicle comprising:means for supplying said selecting and generating means with images of said target object; a controller for controlling the vehicle in response to the determination by said comparing means. 